A new generalization of t-lifting modules

Document Type : Research Paper

Authors

¹ University of Mazandaran, Babolsar, Iran.

² Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran

³ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

⁴ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar

Abstract

In this paper we introduce the concept of

t C C

-modu\-les which is a proper generalization
of (

t

-)lifting modules. Let

M

be a module over a ring

R

.
We call

M

t C C

-module
(related to

t

-coclosed submodules) provided that for every

t

-coclosed submodule

N

M

, there exists a direct summand

K

M

such that

M = N + K

and

N \cap K ≪ K

.
We prove that a module with

(D_{3})

property is

t C C

if and only if every direct summand of

M

t C C

. It is also shown
that an amply supplemented module

M

t C C

if and only if

M

decomposed to

{\overset{―}{Z}}^{2} (M)

and a submodule

L

M

that both of them are

t C C

Keywords